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Numerical study of one-dimensional compression of granular materials. I. Stress-strain behavior, microstructure, and irreversibility

Mohamed Hassan Khalili1,*, Jean-Noël Roux2,†, Jean-Michel Pereira1,‡, Sébastien Brisard1,§, and Michel Bornert1,∥

  • 1Université Paris-Est, Laboratoire Navier, UMR8205, École des Ponts, IFSTTAR, CNRS 6-8 Avenue Blaise Pascal, Cité Descartes, 77455 Marne-la Vallée, France
  • 2Université Paris-Est, Laboratoire Navier, UMR8205, École des Ponts, IFSTTAR, CNRS, 2 Allée Kepler, Cité Descartes, 77420 Champs-sur-Marne, France

  • *mohamed-hassan.khalili@enpc.fr
  • †jean-noel.roux@ifsttar.fr
  • ‡jean-michel.pereira@enpc.fr
  • §sebastien.brisard@ifsttar.fr
  • ∥michel.bornert@enpc.fr
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Phys. Rev. E 95, 032907 – Published 28 March, 2017

DOI: https://doi.org/10.1103/PhysRevE.95.032907

Abstract

The behavior of a model granular material, made of slightly polydisperse beads with Hertz-Mindlin elastic-frictional contacts, in oedometric compression (i.e., compression along one axis, with no lateral strain) is studied by grain-level numerical simulations. We systematically investigate the influence of the (idealized) packing process on the microstructure and stresses in the initial, weakly confined equilibrium state, and prepare both isotropic and anisotropic configurations differing in solid fraction Φ and coordination number z. Φ (ranging from maximally dense to moderately loose), z (which might vary independently of Φ in dense systems), fabric and force anisotropy parameters, and the ratio K0 of lateral stresses σ2=σ3 to stress σ1 in the compression direction are monitored in oedometric compression in which σ1 varies by more than three orders of magnitude. K0 reflects the anisotropy of the assembling process and may remain nearly constant in further loading if the material is already oedometrically compressed (as a granular gas) in the preparation stage. Otherwise, it tends to decrease steadily over the investigated stress range. It is related to force and fabric anisotropy parameters by a simple formula. Elastic moduli, separately computed with an appropriate matrix method, may express the response to very small stress increments about the transversely isotropic well-equilibrated states along the loading path, although oedometric compression proves an essentially anelastic process, mainly due to friction mobilization, with large irreversible effects apparent upon unloading. While the evolution of axial strain ε1 and solid fraction Φ (or of the void ratio e=−1+1/Φ) with axial stress σ1 is very nearly reversible, especially in dense samples, z is observed to decrease (as previously observed in isotropic compression) after a compression cycle if its initial value was high. K0 relates to the evolution of internal variables and may exceed 1 in unloading. The considerably greater irreversibility of oedometric compression reported in sands, compared to our model systems, should signal contact plasticity or damage.

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Numerical study of one-dimensional compression of granular materials. II. Elastic moduli, stresses, and microstructure

Mohamed Hassan Khalili, Jean-Noël Roux, Jean-Michel Pereira, Sébastien Brisard, and Michel Bornert
Phys. Rev. E 95, 032908 (2017)

Article Text

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Phys. Rev. E 95, 032907– Published 28 March, 2017
  • Received 20 November 2016

©2017 American Physical Society

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